This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372321 #12 Feb 16 2025 08:34:06
%S A372321 -1,0,6,81,1620,45765,1671678,74794671,3958829640,241898775273,
%T A372321 16756621904970,1297547591499819,111065107263415308,
%U A372321 10412999996499836541,1061234184094567585326,116812280111404106348415,13810631408232372091755792,1745470697932523785587735249
%N A372321 Expansion of e.g.f. -exp( x + LambertW(-3*x)/3 ).
%H A372321 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372321 a(n) = Sum_{k=0..n} (3*k-1)^(k-1) * binomial(n,k).
%F A372321 G.f.: Sum_{k>=0} (3*k-1)^(k-1) * x^k / (1-x)^(k+1).
%F A372321 a(n) ~ 3^(n-1) * n^(n-1) * exp((exp(-1) - 1)/3). - _Vaclav Kotesovec_, May 06 2024
%o A372321 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x+lambertw(-3*x)/3)))
%o A372321 (PARI) a(n) = sum(k=0, n, (3*k-1)^(k-1)*binomial(n, k));
%Y A372321 Cf. A088957, A360193, A372315, A372316, A372320.
%K A372321 sign
%O A372321 0,3
%A A372321 _Seiichi Manyama_, Apr 27 2024